In this paper, we build the Wong–Zakai approximation for Stratonovich-type stochastic differential equations driven by G-Brownian motion and obtain the quasi-sure convergence rate under Holder norm by a rough path argument. As a corollary, we obtain the quasi-continuity of solutions of random rough differential equations driven by lifted martingales under a sequence of singular measures.

中文翻译：

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G-布朗运动驱动的随机微分方程的Wong-Zakai近似

在本文中，我们建立了由 G-Brownian 运动驱动的 Stratonovich 型随机微分方程的 Wong-Zakai 近似，并通过粗糙路径论证获得了 Holder 范数下的准确定收敛率。作为推论，我们获得了在一系列奇异测度下由提升鞅驱动的随机粗糙微分方程解的准连续性。